MS 150 Statistics midterm • Name:

Riders
6.0
7.5
9.1
9.4
9.7
9.0
10.3
12.0
9.7
10.1
9.8

The RipStik linear regression curve homework and quiz five RipStik learning curve both focused on the recently developed Razor USA LLC RipStik. As Razor is a privately owned company, actual sales figures for the RipStik are not publicly available. RipStiks can be seen as an evolution of the skateboard. The data in the table is millions of skateboarder riders per year in the United States over an eleven year period for skateboarder riders seven years of age and older.

The RipStik linear regression curve homework and quiz five RipStik learning curve both focused on the recently developed Razor USA LLC RipStik. As Razor is a privately owned company, actual sales figures for the RipStik are not publicly available. RipStiks can be seen as an evolution of the skateboard. The data in the table is millions of skateboarder riders per year in the United States over an eleven year period for skateboarder riders seven years of age and older.

1. __________ What level of measurement is the data?
2. __________ Calculate the sample size n for the data.
3. __________ Determine the minimum.
4. __________ Determine the maximum.
5. __________ Calculate the range.
6. __________ Calculate the midrange.
7. __________ Determine the mode.
8. __________ Determine the median.
9. __________ Calculate the sample mean x.
10. 1.54 Freebie: This is the standard deviation sx. If you obtain a different value, then you typed in the wrong data! Calculate the standard deviation sx and check for agreement. [1.5415 to four decimal places]
11. __________ Calculate the sample coefficient of variation CV.
12. __________ If this data were to be divided into five classes, what would be the width of a single class?
13. Determine the frequency and calculate the relative frequency using five classes. Record your results in the table provided.
Frequency table
Riders CUL (cm)Frequency (f)Relative Frequency
Sum:
1. Sketch a frequency histogram chart of the data anywhere it fits, labeling your horizontal axis and vertical axis as appropriate.
2. ____________________ What is the shape of the distribution?
3. ____________________ In 2008 there were an estimated 12.2 million volleyball players in the United States. Use the sample mean x and standard deviation sx calculated above to determine the z-score for 12.2.
4. ____________________ Is the z-score for 12.2 an ordinary or unusual z-score?
5. ____________________ In 2008 there were an estimated 35.9 million runners. Use the sample mean x and standard deviation sx calculated above to determine the z-score for 35.9.
6. ____________________ Is the z-score for 35.9 an ordinary or unusual z-score?

Part II: Linear regression

In the world of entrepreneurship, one will be more successful if one targets a growing sector of the market. Targeting a shrinking sector of the market is a recipe for business contraction and failure. This section of the test asks the basic business question, is the market for skateboards expanding based on the number of skateboarder riders? In the table below, year 0 is 1990, year 8 is 1998, year 10 is 2000, and year 18 is 2008.

YearRiders
86.0
97.5
109.1
119.4
129.7
139.0
1410.3
1512.0
169.7
1710.1
189.8
1. __________ Calculate the slope of the linear regression for the data.
2. __________ Calculate the y-intercept of the linear regression for the data.
3. __________ Use the slope and intercept to predict the the number of skateboard riders this year, in 2010 (use 20 for the year).
4. __________ Use the slope and intercept to predict the year in which there will be 35.9 million skateboard riders.
5. __________ Does the relationship appear to be linear, non-linear, or random?
6. __________ Is the correlation positive, negative, or neutral?
7. __________ Calculate the correlation coefficient r.
8. __________ What is the strength of the correlation: strong, moderate, weak, or none?
9. __________ Calculate the coefficient of determination r².
10. __________ What percent of the variation in the year explains the variation in the number of skateboard riders?
11. __________ Based on the slope and correlation, is this a growing market that would be good to target with a new business?
12. If yes, why yes? If no, why not?